Corollary 21 ([1]}) 
Let \(\phi : \mathcal {X}\rightarrow \mathcal {Y}\)  denote a 1-Lipchitz map between \(m\) -dimensional sets \(\mathcal {X}, \mathcal {Y}\) . Then \(\operatorname{vol}_m(\phi (\mathcal {X})) \le \operatorname{vol}_m(\mathcal {X})\) .

